During a two-hour, closed-door meeting in the basement of the Capitol, Ryan and other GOP leaders urged their troops not to endorse a procedural move to force votes on the Deferred Action for Childhood Arrivals (DACA) program — known as a discharge petition — and instead give leaders more time to forge a compromise that can win 218 Republican votes.

“The next step is to start putting pen to paper and get legislation to the floor,” the Wisconsin Republican told reporters afterwards.

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The promise seems to have bought them some time in their search for an elusive DACA deal that can win the support of centrist immigration reformers and conservative hardliners. Indeed, several moderates who have remained open to signing the petition said after the meeting that they’ll refrain from doing so while GOP leaders seek a compromise.

By the obscure rules of the discharge petition, the supporters hoping to ensure DACA votes this month have until June 12 to gather the 218 signatures needed to force the issue to the floor. And while Ryan indicated there’s no official deadline — “Our new deadline is not to have a deadline,” he said — McCarthy seems to be eying next week as a more concrete target.

“That comes down to the 12th, so we're moving towards getting a bill,” McCarthy told The Hill.

That leaves leadership with just five days to craft legislation they believe can garner 218 GOP votes. Supporters of the petition are two Republican signatures away from the number of members needed to bypass leadership and bring the “Queen of the Hill” rule to the floor.

Ryan and other GOP leaders, who have been scrambling to forge a DACA compromise that would make the discharge petition unnecessary, had hoped to have such an agreement finalized to present to the conference at Thursday’s gathering. Indeed, that was the expectation of some of the Republicans going in.

Rohrabacher, for instance, offered a proposal to offer visas to 50,000 immigrants per year — for a $1 million fee.

Many of those proposals are non-starters in the current DACA debate, however, and many of the moderate Republicans are growing impatient with their leadership’s inaction, both in staging votes and offering an alternative proposal for propping up DACA.

“The buffet’s full. Either starve to death or go get something to eat.”

While many members appeared optimistic they could reach a deal that satisfies all factions of the conference, they also noted the pressure on leadership created by the discharge petition remains a factor in the debate.

“So the threat’s not going to leave,” he added, “so let's see if there's a way to resolve it without that. And if not, then this is going to come to a head.”

Still, most Republicans walked out of the meeting without a clear idea of what lies ahead.

“It's just a mystery, still, whether we’ll be able to get the signatures or whether they'll bring some proposals to the floor,” said Rep. Ileana Ros Lehtinen (R-Fla.), another petition signer. “Some of us are really frustrated to not be able to have a vote.”